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Find the locus of midpoint of family of chords `lamdax+y=5(lamda` is parameter) of the parabola `x^(2)=20y` |
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Answer» Equation of family of chord is `(y-5)+lamda(x-0)=0`, which are concurrent at (0,5). The given parabola is `x^(2)-20y=0`. Let M (h,k) be midpoint of chord. Therefore, equation of such chord is `hx-10(y+k)=h^(2)-20k" "(Using T=S_(1))` This chord is passing through the point (0,5). This chord is passing through the point (0,5). `:." "h^(2)=10k-50` So, locus of M (h,k) is `x^(2)=10(y-5)`. |
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